Introduction

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Welcome!

This website provides interactive results for the forecasting models explored in the paper Estimating Neighborhood Rents using Scraped Data.

The goal of this research is to a.) understand the temporal dynamics of rent estimates in Seattle and b.) forecast the current quarter’s rent levels based off of the prior periods. The focal series of models regress median one-bedroom rent asked values on different specifications of the panel’s correlation structure (i.e. temporal and spatial). All of the candidate models’ posterior distributions are estimated with integrated nested Laplace approximations (INLA) using the default, weakly-informative priors for all model hyperparameters. Throughout the following analyses, the training data are 2017 Q1 up to the prior quarter (i.e. 2018 Q1). The test period is a forecast for the current period and includes comparison to the appropriate median rent estimates for data observed so far in this period.

Most graphics include some level of interactivity, usually either hover-over tooltip information or a slider to control various views of the graphic. Clicking on cases will highlight data elements in most graphics, and double-clicking will reset the graphic.

This page was last updated: 2018-06-04




Table of Contents

Page Description
Distribution density graphic to investigate the distribution of rents among Seattle neighborhoods for each quarter
Panel Time-Series line graphic to show the observed or modeled temporal structure
Spatial Time-Series series of maps to show observed change across time
Model Fit tables of model root mean square error (RMSE), mean absolute error (MAE), and deviance information criterion (DIC) across training and test data

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Observed vs. Smoothed Rent Estimates

Distribution

Panel Time-Series

Spatial Time-Series

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Observed

Non-Spatial AR(1)

Spatial AR(1)

Spatiotemporal AR(1)

Model Fit

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Model Legend

Model abbr. Description
int Quarter fixed intercept
log(med1B) ~ 1 + Qtr
ns Non-spatial tract random effect for each tract, quarter fixed intercept
log(med1B) ~ 1 + Qtr + f(idtract, model = “iid”)
nsar1 Non-spatial tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter
log(med1B) ~ 1 + f(idtract, model = “iid”) + f(idqtr, model = “ar1”) + , f(idqtr1, model = “iid”)
bym Spatial intrinsic conditional autoregressive (ICAR) tract random-effect, non-spatial i.i.d tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter
log(med1B) ~ 1 + f(idtract, model = “bym”, scale.model = T, graph = “../output/seatract.graph”) + , f(idqtr, model = “ar1”) + f(idqtr1, model = “iid”)
spt Spatial intrinsic conditional autoregressive (ICAR) tract random-effect, non-spatial i.i.d tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter, i.i.d. random effect for tract-quarter (space-time interaction)
log(med1B) ~ 1 + f(idtract, model = “bym”, scale.model = T, graph = “../output/seatract.graph”) + , f(idqtr, model = “ar1”) + f(idqtr1, model = “iid”) + f(idtractqtr, , model = “iid”)

Accuracy and Information Criteria

train_test int_rmse ns_rmse nsar1_rmse bym_rmse spt_rmse
Test 306.1430 213.8335 206.3276 199.2464 199.3335
Training 324.2904 145.9141 145.9562 147.2614 146.1541



train_test int_mae ns_mae nsar1_mae bym_mae spt_mae
Test 250.5052 151.4203 148.5778 141.9268 141.8826
Training 261.4572 100.9766 100.6866 102.2933 101.5405



train_test int_DIC ns_DIC nsar1_DIC bym_DIC spt_DIC
Training -230.4437 -872.8758 -871.7695 -874.5012 -876.0232



train_test int_WAIC ns_WAIC nsar1_WAIC bym_WAIC spt_WAIC
Training -230.0655 -845.3891 -844.3364 -847.8052 -848.7696

Hyperparameters

Non-Spatial AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 94.4504 6.3451 82.3883 94.3203 107.3392 94.1694
Precision for idtract 30.7244 4.2509 23.1165 30.4724 39.8230 30.0119
Precision for idqtr 3704.6708 3774.0461 555.1018 2589.2781 13619.6753 1361.1160
Rho for idqtr 0.2605 0.3581 -0.4721 0.2856 0.8484 0.3946
Precision for idqtr1 14301.7423 17584.8007 273.1949 8209.2304 61744.3916 355.9311



Spatial AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 93.8803 6.3335 81.9178 93.7135 106.8512 93.4437
Precision for idtract (iid component) 89.3900 21.4776 54.3609 86.9820 138.4270 82.4034
Precision for idtract (spatial component) 90.8715 29.0756 47.3037 86.3832 160.0849 78.1261
Precision for idqtr 4002.4514 4216.6368 591.5302 2748.9778 15035.0510 1437.1243
Rho for idqtr 0.2753 0.3541 -0.4591 0.3044 0.8495 0.4277
Precision for idqtr1 13191.6565 16518.6337 232.6458 7429.0684 57455.3465 282.3816



Spatiotemporal AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 94.2806 6.3930 82.2396 94.0988 107.4066 93.7844
Precision for idtract (iid component) 89.1937 21.4138 54.4062 86.7437 138.1697 82.0766
Precision for idtract (spatial component) 90.8342 29.0375 47.2612 86.3834 159.9507 78.1852
Precision for idqtr 3899.6816 4044.5959 581.8963 2700.4274 14499.5978 1414.3937
Rho for idqtr 0.2664 0.3557 -0.4652 0.2928 0.8482 0.4061
Precision for idqtr1 13557.9491 16918.7848 238.6252 7654.8006 58780.1603 290.7391
Precision for idtractqtr 19372.1292 18643.6023 1360.6730 13931.8141 68592.3473 3757.3146

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Non-Spatial AR(1)

Spatial AR(1)

Spatiotemporal AR(1)